Inverse topology in MV-algebras

Abstract

We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra $A$ and show that the set of all minimal prime ideals of $A$, namely ${\rm Min}(A)$, with the inverse topology is a compact space, Hausdorff, $T_0$-space and $T_1$-space. Furthermore, we prove that the spectral topology on ${\rm Min}(A)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on ${\rm Min}(A)$ is finer than the inverse topology on ${\rm Min}(A)$. Finally, by open sets of the inverse topology, we define and study a congruence relation of an MV-algebra.

Keywords

• minimal prime
• spectral topology
• inverse topology
• congruence